Currently (2021) the rule is—
One mene ends and the next begins when the last boule thrown in the mene comes to rest.
Before the 2020 rules changes, one of the frequently-asked questions about petanque was “When does a mene begin and end?” At that time petanque used two different models of when menes (“ends”, “rounds”) begin and end, so it’s not surprising that players were confused.
The official FIPJP rules of the game used the FIPJP Rules model. Under this model, a mene ended with the agreement of points, and the next mene started with the throw of the jack. Between the agreement of points and the throw of the jack, there was a break — a period of time between the menes.
A different model was used for time-limited games. In the Time-Limited Games model a single event marked the end of one mene and the start of the next. The event was specified by competition organizers in the rules for the time-limited games in the competition. For many years the Eurocup specified that the dividing event was the agreement of points. That changed a few years ago; now the Eurocup rule is: “A new end is considered to have started as soon as the last boule from the previous end has been played.” That rule was based on the one-minute rule in Article 21:
Once the jack is thrown, each player has the maximum duration of one minute to play his boule. This short period of time starts from the moment that the previously played boule or jack stops…
The Petanque New Zealand umpire’s guide gives a clear explanation of the rule.
When the time signal is sounded, if all boules of the end have been played and have come to a stop… that end has finished (regardless of measuring and deciding points) and you have officially started the new end.
In 2020, the international umpires who write the rules decided that they wanted to have a single rule that would apply to all games— “normal” games as well as time-limited games. To do this, they discarded the old FIPJP model and adopted the time-limited games model for all games. So now (after 2020) players need to remember only one simple rule (found in Article 33) which I will paraphrase this way.
A mene ends (and the next begins) when the last boule thrown in the mene comes to rest on the terrain.
Note that if a thrown boule hits the jack out-of-bounds, the mene does not end when the jack crosses the dead-ball line; it ends when the thrown boule comes to rest on the terrain. If the thrown boule also rolls across the dead-ball line; the mene ends when the boule crosses the dead-ball line.